Reeb spaces of smooth functions on manifolds II

Abstract

The Reeb space of a continuous function is the space of connected components of the level sets. In this paper we characterize those smooth functions on closed manifolds whose Reeb spaces have the structure of a finite graph. We also give several explicit examples of smooth functions on closed manifolds such that they themselves or their Reeb spaces have some interesting properties.

11 pages, 6 figures, continuation of the previous paper "Reeb spaces of smooth functions on manifolds"